Abstract

A model is presented that endogenizes the two most important sources of technological change –uncertainty, and technological learning through re-search and development (R&D) and learning by doing (investments)– into an intertemporal optimization framework. Mathematically, the resulting prob-lem is one of non-convex, non-smooth, stochastic optimization. The simple, stylized sectoral (energy) model includes one demand and one resource cat-egory. The model selects from three competing technologies, which differ in their current costs and in their (uncertain) potentials for future cost reduc-tions through learning. The resulting model fully endogenizes the process of technological change, which is driven by expected, but uncertain, returns from investments into R&D and niche-market applications. These in turn can render new technologies increasingly competitive, ultimately leading to pervasive diffusion. The model, while definitely oversimplified, nevertheless allows several robust conclusions. First, it was possible to find an opera-ble analytical solution for an optimization problem that simultaneously in-volves stochasticity (uncertainty) as well as non-convexity (increasing returns through technological learning). Second, the S-shaped patterns of technolog-ical entry and diffusion endogenously generated by the model are consistent with those observed historically and in the empirical literature on technologi-cal diffusion. Third, the model illustrates the possibility of wide-ranging tech-nological outcomes resulting from even small differences in initial conditions and the (uncertain) rates of technological learning. Fourth, the resulting dif-fusion of new technologies of our model can yield pronounced discontinuities in the environmental performance of technologies. For instance, future emis-sions could decline radically even in absence of environmental constraints. 1 Fifth, and perhaps most importantly, the model demonstrates an entirely endogenous mechanism of technological change in which technologies that appear to be extremely economically unattractive from today's perspective (e.g. a factor 40 more expensive) can diffuse into the market under both criteria of uncertainty and intertemporal optimization (cost minimization), if upfront investments into R&D and niche market applications are made. These are shown also to constitute an optimal contingency policy vi a vis uncertainty in future energy demand and possible (uncertain) emergence of environmental constraints (e.g., a tax on carbon emissions).